Optimal Penalized Function-on-Function Regression under a Reproducing Kernel Hilbert Space Framework.
TL;DR: A function-on-function regression model that can be used to analyze functional data where the response and predictor variables are both functions of time, location, or some other covariate is presented and the estimator of the 2D coefficient function is the optimizer of a form of penalized least squares.
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Abstract: Many scientific studies collect data where the response and predictor variables are both functions of time, location, or some other covariate. Understanding the relationship between these functiona...
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Citations
Optimal prediction for additive function-on-function regression
TL;DR: In this paper, the authors consider the additive function-on-function regression model, a type of nonlinear model that uses an additive relationship between the functional outcome and functional covariate.
High-Dimensional Spatial Quantile Function-on-Scalar Regression
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Low-Rank Covariance Function Estimation for Multidimensional Functional Data
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From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas
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TL;DR: Functional data analysis (FDA) is a branch of statistics on modeling infinite dimensional random vectors residing in functional spaces as discussed by the authors, which has become a major research area for Journal of Multivariate Analysis.
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Function-on-function quadratic regression models
Yifan Sun,Qihua Wang,Qihua Wang +2 more
TL;DR: Methods to estimate the coefficient functions, predict unknown response and test significance of the quadratic term are developed in functional principal component regression paradigm and asymptotic theories for these approaches are established.
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Grace Wahba
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TL;DR: In this paper, a theory and practice for the estimation of functions from noisy data on functionals is developed, where convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a number of problems within this framework.
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